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Silicon detectors with a fine segmentation (micropixel and microstrip) are the main type of detectors used in the inner trackers of Large Hadron Collider (LHC) experiments. Due to the high luminosity of the LHC machines they are required to have a fast response to fit the short shaping time of 20 ns and to be radiation hard. Evaluation of silicon microstrip detectors developed for the ATLAS silicon tracker and carried out under collaboration of CERN and Ioffe Physico-Technical Institute has shown the reversal of the pulse polarity in the detector response to short-range radiation. Since the negative signal is of about 30%-60% of the maximal positive one, the effect strongly reduces the charge collection efficiency even in nonirradiated detectors. The investigation presents the consideration of the origin of a negative response in Si microstrip detectors and the experimental proof of the model. The study of the effect has been carried out using "baby" strip detectors with a special design: each strip has a window in a metallization, which covers the p+ implant. The scan of a laser across the strips clearly shows that the negative response is observed along the scan in the interstrip gap. As soon as the light spot is placed on the strip p+ implant the negative response disappears and the value of the charge collected by the active strip proportionally increases. A phenomenological model considers the origin of the negative response as the effect of carrier trapping at the Si-SiO2 interface between the strips.